598 REGNAULT ON THE 
tas ~, e=0; the curve is then a tangent to the axis of the ¢: 
on leaving this point towards the positive ¢, the curve turns its 
convexity towards the axis of ¢, and presents a point of in- 
m (log a — 
flexion for ¢= ae 2s) ; lastly, it is one of the asymptotes 
1 
to the straight line e= aa”, parallel to the axis of the ¢. The 
other branch is one of the asymptotes to the same straight line 
1 
e=aa", and to the straight line ¢ = — = parallel to the axis of 
the e. 3 
Lastly, M. Biot has given a new mode of interpolation*, which 
he has applied to the formation of a table of the elastic forces of 
aqueous vapour between —20° and 220°, trusting to the ex- 
periments of M. Gay-Lussac for temperatures below 100°, and 
to the experiments of MM. Dulong and Arago for higher tem- 
peratures. The formula adopted by M. Biot is analogous to 
that of Prony; only that M. Biot makes the sum of the expo- 
nents equal the logarithm of the elastic force, and not the elastic 
force itself: he perceived that it could be confined to three 
terms, even supposing the base of one of the exponents to equal 
1; so that he adopts the following formula,— 
loge = a+ bai+cf. 
The five constant quantities which enter into this expression 
are determined by five observations conveniently distanced in 
the scale of temperatures. I have adopted M. Biot’s mode of 
interpolation, which appears to me applicable with advantage to 
a large number of physical phanomena, and particularly to the 
relations which exist between the elastic forces of vapours and 
the temperatures. 
I do not propose at present to calculate a formula which shall 
represent the phenomenon in its whole extent ; the observations 
which I made at high pressures are not sufficiently complete, 
they ought to be carried much further: these observations pre- 
sent, besides, particular difficulties, which I shall presently point 
out, and which prevent me from regarding them as perfectly 
satisfactory. At present I shall only notice the elastic forces of 
aqueous vapour between 0° and 100°. I determine the five con- 
stant quantities which enter the formula 
loge=a-+ ba,'+ cB,’ 
* Comptes Rendus de ? Académie, t. xii. p. 150. 
